Castelli, Benedetto, Of the mensuration of running waters, 1661

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            <p type="main">
              <s>
                <pb xlink:href="068/01/066.jpg" pagenum="52"/>
                <emph type="italics"/>
              the fourth
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              Theorem
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              of this, with its Table, and the uſe there­
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              of annexed.
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              </s>
            </p>
            <p type="head">
              <s>
                <emph type="italics"/>
              COROLLARIE
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              </s>
            </p>
            <p type="main">
              <s>Hence it followeth, that when a River increaſeth in quick
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              height by the addition of new water, it alſo increaſeth in ve­
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              locity; ſo that the velocity hath the ſame proportion to the velo­
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              city that the quick height hath to the quick height; as may be
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              demonſtrated in the ſame manner.</s>
            </p>
            <p type="head">
              <s>PROPOS. III. PROBLEME II.</s>
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            <p type="main">
              <s>
                <emph type="italics"/>
              Achanel of Water being given whoſe breadth exceeds not
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              twenty Palms, or thereabouts, and whoſe quick beight
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              is leſs than five Palms, to meaſure the quantity of the
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              Water that runneth thorow the Chanel in a time
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              given.
                <emph.end type="italics"/>
              </s>
            </p>
            <p type="main">
              <s>Place in the Chanel a Regulator, and obſerve the quick
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              height in the ſaid Regulator; then let the water be turned
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              away from the Chanel by a Chanellet of three or four Palms
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              in breadth, or thereabouts: And that being done, meaſure the
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              quantity of the water which paſſeth thorow the ſaid Chanellet,
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              as hath been taught in the ſecond Propoſition; and at the ſame
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              time obſerve exactly how much the quick height ſhall be abated
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              in the greater Chanel, by means of the diverſion of the Chancl­
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              let; and all theſe particulars being performed, multiply the quick
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              height of the greater Chanel into it ſelf, and likewiſe multiply
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              into it ſelf the leſſer height of the ſaid bigger Chanel, and the
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              leſſer ſquare being taken, from the greater, the remainder ſhall
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              have the ſame proportion to the whole greater ſquare, as the wa­
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              ter of the Chanellet diverted, hath to the water of the bigger
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              Chanel: And becauſe the water of the Chanellet is known by
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              the Method laid down in the firſt Theorem, and the terms of the
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              Theorem being alſo known, the quantity of the water which run­
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              neth thorow the bigger Chanel, ſhall be alſo known by the Gol­
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              den
                <emph type="italics"/>
              R
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              ule, which was that that was deſired to be known. </s>
              <s>We
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              will explain the whole buſineſs by an example.</s>
            </p>
            <p type="main">
              <s>Let a Chanel be, for example, 15 Palms broad, its quick height
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              before its diverſion by the Chanellet ſhall be ſuppoſed to be 24
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              inches; but after the diverſion, let the quick height of the Chanel
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              be onely 22 inches. </s>
              <s>Therefore the greater height to the leſſer,
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              is as the number 11. to 12. But the ſquare of 11. is 121, and the
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              ſquare of 12. is 144, the difference between the ſaid leſſer </s>
            </p>
          </chap>
        </body>
      </text>
    </archimedes>
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